Bolton, J. Stuart

Kang, Yeon June

Song, Bryan

English

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Purdue UniversityPurdue e-PubsPublications of the Ray W. Herrick Laboratories School of Mechanical Engineering12-1999Effect of Circumferential Edge Constraint on theTransmission Loss of Glass Fiber MaterialsJ. Stuart BoltonPurdue University, bolton@purdue.eduBryan SongYeon June KangSeoul National UniversityFollow this and additional works at: http://docs.lib.purdue.edu/herrickThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Bolton, J. Stuart; Song, Bryan; and Kang, Yeon June, "Effect of Circumferential Edge Constraint on the Transmission Loss of GlassFiber Materials" (1999). Publications of the Ray W. Herrick Laboratories. Paper 16.http://docs.lib.purdue.edu/herrick/16Effect of Circumferential Edge Constraint on the Transmission    Loss of Glass Fiber MaterialsBryan H. Song and J. Stuart BoltonRay W. Herrick LaboratoriesPurdue UniversityYeon June KangSeoul National UniversityPurdue University Herrick LaboratoriesIntroductionWh I ti ti f d t i t ff t l• y: nves ga on o e ge cons ra n e ec on samp esplaced in a modified standing wave tube (B. H. Song et al.,JASA 1999, In Press; J. S. Bolton et al., SAE 1997).• How: Comparison of TL and impedance measurementswith FEM predicted results using an axisymmetric modelCOMET / SAFE (Y. J. Kang et al., JASA 1999).Demonstration of how the materials’ mechanical andphysical properties control TL• What: Implications for design of low frequency noisecontrol barriers following from constraint of porous liningmaterials around their edges.Experimental Setup High Frequency TubeDual ChannelSignal AnalyzerB & K T 2032Computer   ype Signal AmplifierCH BCH A SignalGeneratorMicrophonesTwo-MicrophoneImpedance Measurement TubeB & K Type 4206NewSampleHolderAnechoicTermination• 2.9 cm diameter samples, 7.5 cm deep• Aviation grade glass fiber, 9.61 Kg/m3Transfer Matrix Approach I1 2 3 4AB DCPTTP  1211xx=0 x=ddxx VTTV  222102211 TT         (symmetry)Four Equations121122211  TTTT      (reciprocity)• Solve for transfer matrix elementsTransfer Matrix Approach II  1 eTTTR jkdaa 0022211211001ceTTTcR jkdaa2221001211 TcTcTT  21 aR• Anechoic Reflection Coefficient2221001211 TcTcTTR aA h i T i i C ffi i taan RRZ112221012112TcTTTeTjkda)/1log(10 2aTTL • nec o c ransm ss on oe c en0 cAnechoic Transmission Loss40Experiment3035 Prediction using FEM (with edge constraint)Prediction without edge constraint2025 (dB)1015TLIncrease in TL5 Shearing mode  due to edge constraint102 103 1040Frequency (Hz)Anechoic Absorption Coefficient0 910.70.8.0.50.6on coefficient0.30.4Absorptio00.10.2ExperimentPrediction using FEM (with edge constraint)Prediction without edge constraint102 103 104Frequency (Hz)Surface Normal Impedance810ExperimentPrediction using FEM (with edge constraint)246Re(Zn) Prediction without edge constraint102 103 1040Frequency (Hz)50m(Zn)102 103 104-5ImFrequency (Hz)• Change from mass-like reactance to stiffness reactanceEstimation of Material Mechanical Properties• Error surface • Objective Function0.420.440.460.48+imim iiiiJ 22FEM22FEMTL|TLTL|||0.380.4son s ratio0.4870.495mm iiBulk Measured / Porosity Tortuosity Young’s Loss Poisson0.340.36Poiss 0.5020.5090.5160.5230.5160.523density (kg/m3) Predicted Flowresistivity(MKS Rayls/m)modulus (Pa)factor ratio9.61 24400 / 40000 0.99 1.1 8250 0.5 0.457000 7500 8000 8500 9000 95000.30.32Youngs modulus [Pa]0.5370.559+   Minimum locationTransmission Loss Absorption Coefficient• Shear modulus controls minimum location in TL curve•  G = E/2(1+v)= 2845 Pa140      0.60.70.80.9fficient2530350.30.40.5Absorption coef1520TL (dB)102 103 10400.10.2F (H )E=8250 Pa v=0.45E=7397 Pa v=0.3 E=6828 Pa v=0.2 E=6259 Pa v=0.1 102 103 1040510E=8250 Pa v=0.45E=7397 Pa v=0.3 E=6828 Pa v=0.2 E=6259 Pa v=0.1 requency zFrequency (Hz)Variation of Shear Modulus• As shear modulus increases, the minimum location moves to higher frequencies3540G=1466 PaG=2845 PaG=4224 Pa      25301520TL510102 103 1040Frequency (Hz)Flow Resistivity Loss Factor• Flow resistivity controls • Loss factor controls depth of TL minimum4040Flow resistivity=20000 MKS Rayls/mTL in low and high frequency limit   253035253035   Flow resistivity=40000 MKS Rayls/mFlow resistivity=60000 MKS Rayls/m101520TL (dB)1520TL (dB)102 103 10405F (H )loss factor = 0.1loss factor = 0.3loss factor = 0.5102 103 1040510requency zFrequency (Hz)Axial Particle Velocity at the Front of Sample• Solid phase (unconstrained) • Fluid phase (unconstrained)0 .60 .811 .2velocity (m/s)|0 .40 .60 .81velocity (m/s)|05 0 01 0 0 01 5 0 02 0 0 000 .0 0 50 .0 10 .0 1 50 .20 .4F r e q u e n c y  ( H z )r a d iu s  ( m )|Fluid v05 0 01 0 0 01 5 0 02 0 0 000 .0 0 50 .0 10 .0 1 500 .2F r e q u e n c y  ( H z )r a d iu s  ( m )|Solid v1 .50 .8• Solid phase (constrained) • Fluid phase (constrained)2 0 0 00 0 10 .0 1 500 .51|Fluid velocity (m/s)|2 0 0 00 0 10 .0 1 500 .20 .40 .6|Solid velocity (m/s)|05 0 01 0 0 01 5 0 000 .0 0 5.F r e q u e n c y  ( H z )r a d iu s  ( m )05 0 01 0 0 01 5 0 000 .0 0 5.F r e q u e n c y  ( H z )r a d iu s  ( m )Solid Phase of Constrained Sample (SDX)• 200 Hz • 1100 Hz• 500 Hz • 1800 HzFluid Phase of Constrained Sample (ADX)• 200 Hz • 1100 Hz• 500 Hz • 1800 HzEffect of Sample SizeExperimental Setup for Low Frequency Tube     Dual ChannelSignal AnalyzerComputerB & K Type 2032Signal AmplifierCH BCH A SignalGeneratorMicrophonesTwo-MicrophoneImpedance Measurement TubeB & K Type 4206NewSampleHolderAnechoicTermination    • 10 cm diameter samples, 7.5 cm deep• Aviation grade glass fiber, 9.61 Kg/m3Transmission Loss (50 Hz - 1600 Hz)40Experiment     FEM (G=1810 Pa)3035  2025TL(dB)1015T05102 103Frequency(Hz)Transmission Loss (100 Hz - 6400 Hz)40Experiment (large)3035 FEM (G=1810 Pa)   Unconstrained caseExperiment (small)FEM (G=2845 Pa)   2025(dB)• 10 cm samples very nearly approximates1015TL(  unconstrained case05102 103 104Frequency(Hz)airairfoamAcoustical performances of fibrous layers such asConclusionstransmission loss and absorption coefficient are affected byconstraint on the boundary of the samples. The edge constraint effect is well predicted by usingporoelastic FEM model (COMET/SAFE). Light and stiff fibrous materials combined with edge constraintmechanisms may enable us to design, light, high performancelow frequency noise control barriers.

Effect of Circumferential Edge Constraint on the Transmission Loss of Glass Fiber Materials

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Effect of Circumferential Edge Constraint on the Transmission Loss of Glass Fiber Materials

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